International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On Multiple Linear Approximations

Alex Biryukov
Christophe De Canni\`ere
Michael Quisquater
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Abstract: In this paper we study the long standing problem of information extraction from multiple linear approximations. We develop a formal statistical framework for block cipher attacks based on this technique and derive explicit and compact gain formulas for generalized versions of Matsui's Algorithm 1 and Algorithm 2. The theoretical framework allows both approaches to be treated in a unified way, and predicts significantly improved attack complexities compared to current linear attacks using a single approximation. In order to substantiate the theoretical claims, we benchmarked the attacks against reduced-round versions of DES and observed a clear reduction of the data and time complexities, in almost perfect correspondence with the predictions. The complexities are reduced by several orders of magnitude for Algorithm 1, and the significant improvement in the case of Algorithm 2 suggests that this approach may outperform the currently best attacks on the full DES algorithm.
  title={On Multiple Linear Approximations},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / linear cryptanalysis, multiple linear approximations, maximum likelihood decoding},
  note={ 12471 received 23 Feb 2004},
  author={Alex Biryukov and Christophe De Canni\`ere and Michael Quisquater},